the rational expression \frac{130x}{100 - x} describes the cost, in millions of dollars, to inoculate x percent of the population against a particular strain of flu. complete parts a. through c.
a.evaluate the expression for x = 40, x = 70, and x = 90. describe the meaning of each evaluation in terms of percentage inoculated and cost.
it costs $\square$ million to inoculate 40\% the population.
it costs $\square$ million to inoculate 70\% the population.
it costs $\square$ million to inoculate 90\% the population.
(round to two decimal places as needed.)
b.for what value of x is the expression undefined? select the correct choice below and fill in any answer boxes within your choice.
a. the rational expression is undefined for x = $\square$.
b. the rational expression is defined for all real numbers.
c.what happens to the cost as x approaches 100\%? how can you interpret this observation?
a. the cost increases at a steady rate. a very large amount of money will be enough to inoculate 100\% of the population.
b. the cost is constant. it costs the same to inoculate 100\% of the population as it does to inoculate 90\% of the population.
c. the cost decreases. as you near 100\% of the population inoculated the cost starts to decrease.
d. the cost keeps rising. no amount of money will be enough to inoculate 100\% of the population.

Question

Accepted Answer

# Explanation:
## Step1: Evaluate for $x = 40$
Substitute $x = 40$ into $\frac{130x}{100 - x}$.
$$
\begin{align*}
\frac{130\times40}{100 - 40}&=\frac{5200}{60}\
&=\frac{260}{3}\
&\approx86.67
\end{align*}
$$
## Step2: Evaluate for $x = 70$
Substitute $x = 70$ into $\frac{130x}{100 - x}$.
$$
\begin{align*}
\frac{130\times70}{100 - 70}&=\frac{9100}{30}\
&=\frac{910}{3}\
&\approx303.33
\end{align*}
$$
## Step3: Evaluate for $x = 90$
Substitute $x = 90$ into $\frac{130x}{100 - x}$.
$$
\begin{align*}
\frac{130\times90}{100 - 90}&=\frac{11700}{10}\
&= 1170
\end{align*}
$$
## Step4: Find when the expression is undefined
A rational expression $\frac{a}{b}$ is undefined when $b = 0$. For $\frac{130x}{100 - x}$, set $100 - x=0$, then $x = 100$.
## Step5: Analyze the behavior as $x\to100$
As $x$ approaches $100$ from the left ($x<100$), $100 - x$ approaches $0$ from the positive side. So $\frac{130x}{100 - x}$ (where $x$ is close to $100$)  will be a very large positive number. This means the cost increases without bound.

# Answer:
a. When $x = 40$, it costs $\$86.67$ million; when $x = 70$, it costs $\$303.33$ million; when $x = 90$, it costs $\$1170$ million.
b. The rational expression is undefined for $x = 100$.
c. As $x$ approaches $100\%$, the cost increases without bound. So the answer is A. The cost increases at a steady rate. A very large amount of money will be enough to inoculate $100\%$ of the population.

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Question

Explanation:

Step1: Evaluate for \(x = 40\)

Step2: Evaluate for \(x = 70\)

Step3: Evaluate for \(x = 90\)

Step4: Find when the expression is undefined

Step5: Analyze the behavior as \(x\to100\)

Answer: